Additive Forms of Degree 2^{l} Hemar Godinho

In this paper we prove that if f, g is a pair of additive forms of degree k = 2^{l}, l ≥ 2,

\begin{matrix}f = a_{1}x_{1}^{k} + ⋯ + a_{n}x_{n}^{k} \\ g = b_{1}x_{1}^{k} + ⋯ + b_{n}x_{n}^{k} \end{matrix}

with rational coefficients and in n ≥ 16k^{2} − 26k + 1 variables, then f, g have common p-adic zeros for all prime p.